Building on similar ideas, the work in [1]} investigates the Gromov-Wasserstein distance for object matching, and the authors in [2]} propose an efficient algorithm to compute the Gromov-Wasserstein distance and the barycenter of pairwise dissimilarity matrices. The algorithm uses entropic regularization and Sinkhorn projections, as proposed by [3]}. Later, the authors in [4]} build on this work to propose a distance for graphs and signals living on these graphs. The problem is given as a combination between the Gromov-Wasserstein of graph distance matrices and the Wasserstein distance of graph signals. Then, the work in [5]} proposes a method based on Gromov-Wasserstein which simultaneously learns the graph alignment and the embeddings of graph nodes. The node embeddings are derived using optimal transport, which in turn helps in the graph matching task. The authors follow up on [6]} by devising a scalable version of Gromov-Wasserstein distance for graph partitioning and matching. However, while the above methods solve the alignment problem using optimal transport, the simple distances between aligned graphs do not take into account the global structure of the graph, which is important for proper graph comparison.
